What are proper factors?

Answer 1

Factors are the numbers that evenly divide into a given number.

Proper factors are all the factors of the number except the number itself. Some definitions do not allow the number 1, either. If you distinguish between proper factors and proper divisors, proper factors do not include 1, but proper divisors do.

Examples:

All factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

Proper factors of 54 are 2, 3, 6, 9, 18, and 27.

Proper divisors of 54 are 1, 2, 3, 6, 9, 18, and 27.

All factors of 9 are 1, 3, and 9.

Proper factors of 9 are only 3.

Proper divisors of 9 are 1 and 3.

All factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Proper factors of 30 are 2, 3, 5, 6, 10, and 15.

Proper divisors of 30 are 1, 2, 3, 5, 6, 10, and 15.

All factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Proper factors of 100 are 2, 4, 5, 10, 20, 25, and 50.

Proper divisors of 100 are 1, 2, 4, 5, 10, 20, 25, and 50.

All factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Proper factors of 120 are 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, and 60.

Proper divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, and 60.